Problem $4$: A chip that is of length $L=5mm$ on a side and thickness $t=1mm$ is encased in a ceramic substrate, and its exposed surface is convectively cooled by a dielectric liquid for which $h=150\frac{W}{m^2}-K$ and $T_{}=20C.$

In the off$-$mode the chip is in thermal equilibrium with the coolant $(T_i=T_{}).$ When the chip is energized, however, its temperature increases until a new steady state is established. For purposes of analysis, the energized chip is characterized by uniform volumetric heating with $q^{}=9{10}^6\frac{W}{m^3}.$ Assuming an infinite contact resistance between the chip and substrate and negligible conduction resistance within the chip, determine the steady$-$state chip temperature $T_f.$ Following activation of the chip, how long does it take to come within $1C$ of this temperature? The chip density and specific heat are $=2000k\frac{g}{m^3}$ and $c=700\frac{J}{k}g-K,$ respectivelv